On the Fine Structure of QCD Confining String
This paper had been withdrawn because the prime reported effect had not been confirmed in further investigations (see arXiv:0812.4488 [hep-lat]).
hep-lat↗
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Lattice renormalisation of O(a) improved heavy-light operators: an addendum
The analytical expressions and the numerical values of the renormalisation constants of dimension 3 static-light currents are given at one-loop order of perturbation theory in the framework of Heavy Quark Effective Theory and with an improved gauge action: the static quark is described by the HYP-smeared action and the light quark is of Wilson kind. This completes a work started few years ago and is actually an intermediate step in the measurement of the decay constants $f_{B}$ and $f_{B_{s}}$ by the European Twisted Mass Collaboration [arXiv:1107.1441[hep-lat]].
hep-lat↗
Instantaneous interquark potential in generalized Landau gauge in SU(3) lattice QCD: a possible gauge for the quark potential model
We investigate "instantaneous interquark potential", an interesting gauge-dependent quantity defined from the spatial correlator $<\mathrm{Tr} [U_4^\dagger(s)U_4(s')]>$ of the temporal link-variable $U_4$, in detail in generalized Landau gauge using SU(3) quenched lattice QCD. While the instantaneous potential has no linear part in the Landau gauge, in the Coulomb gauge, it is expressed by the Coulomb plus linear potential, where the slope is 2-3 times larger than the physical string tension, and the lowest energy state is considered to be a gluon-chain state. Using the generalized Landau gauge, we find that the instantaneous potential can be continuously described between the Landau and the Coulomb gauges, and it approximately reproduces the physical interquark potential in a specific intermediate gauge, which we call "$λ_C$-gauge". This $λ_C$-gauge is expected to provide a quark-potential-model picture, where dynamical gluons do not appear. We also investigate $T$-length terminated Polyakov-line correlator and its corresponding "finite-time potential" in generalized Landau gauge.
hep-lat↗
Multi-Higgs U(1) Lattice Gauge Theory in Three Dimensions
We study the three-dimensional compact U(1) lattice gauge theory with $N$ Higgs fields numerically. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. For N=2, the system has a second-order phase transition line $\tilde{c}_1(c_2)$ in the $c_2$(gauge coupling)$-c_1$(Higgs coupling) plane, which separates the confinement phase and the Higgs phase. For N=3, the critical line is separated into two parts; one for $c_2 \alt 2.25$ with first-order transitions, and the other for $c_2 \agt 2.25$ with second-order transitions.
cond-mat.supr-con↗
Finite Element Analysis of the Schroedinger Equation
The purpose of this work is to test the application of the finite element method to quantum mechanical problems, in particular for solving the Schroedinger equation. We begin with an overview of quantum mechanics, and standard numerical techniques. We then give an introduction to finite element analysis using the diffusion equation as an example. Three numerical time evolution methods are considered: the (tried and tested) Crank-Nicolson method, the continuous space-time method, and the discontinuous space-time method.
hep-lat↗
Spectrum of Yang-Mills Theory in D=3+1
We give a comparison of the spectrum of Yang-Mills theory in $D=3+1$, recently derived with a strong coupling expansion, with lattice data. We verify excellent agreement also for 2$^{++}$ glueball. A deep analogy with the $D=2+1$ case is obtained and a full quantum theory of this approach is also given.
hep-th↗
Bs and Bc mesons in lattice QCD with exact chiral symmetry
We determine the masses and decay constants of the pseudoscalar mesons Bs and Bc, and also the masses of the vector mesons Bs^* and Bc^*, in quenched lattice QCD with exact chiral symmetry. For 100 gauge configurations generated with single-plaquette action at beta = 7.2 on the 32^3 x 60 lattice, we compute point-to-point quark propagators for 33 quark masses in the range [0.01, 0.85], and measure the time-correlation functions of pseudoscalar and vector mesons. The inverse lattice spacing and the charm quark bare mass are determined using the mass and decay constant of eta_c(2980). The bare masses of s and b quarks are chosen such that the masses of the corresponding vector mesons are in good agreement with phi(1020), and Upsilon(9460) respectively. Our results are: m_{Bs} = 5385(27)(17) MeV, f_{Bs} = 253(8)(7) MeV, m_{Bc} = 6278(6)(4) MeV, f_{Bc} = 489(4)(3) MeV, m_{Bs^*} = 5424(28)(19) MeV, and m_{Bc^*} = 6315(6)(5) MeV.
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Large statistics study of the topological charge distribution in the SU(3) gauge theory
We present preliminary results for a high statistics study of the topological charge distribution in the SU(3) Yang-Mills theory obtained by using the definition of the charge suggested by Neuberger fermions. We find statistical evidence for deviations from a gaussian distribution. The large statistics required has been obtained by using PCs of the INFN-GRID.
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Perturbative spectrum of a Yukawa-Higgs model with Ginsparg-Wilson fermions
A Yukawa-Higgs model with Ginsparg-Wilson (GW) fermions, proposed recently by Bhattacharya, Martin and Poppitz as a possible lattice formulation of chiral gauge theories, is studied. A simple argument shows that the gauge boson always acquires mass by the Stückelberg (or, in a broad sense, Higgs) mechanism, regardless of strength of interactions. The gauge symmetry is spontaneously broken. When the gauge coupling constant is small, the physical spectrum of the model consists of massless fermions, massive fermions and \emph{massive} vector bosons.
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Dual representation of Polyakov loop in 3d SU(2) lattice Yang-Mills theory
We consider the expectation value of a Polyakov loop in 3d SU(2) lattice Yang--Mills theory and transform it to the dual representation in terms of sums over spins. The spin dependence of the amplitudes is computed explicitly by a graphical method. We also determine the asymptotic (large spin) limit of the amplitude factors.
hep-lat↗
An exact string representation of 3d SU(2) lattice Yang--Mills theory
We show that 3d SU(2) lattice Yang--Mills theory can be cast in the form of an exact string representation. The derivation starts from the exact dual (or spin foam) representation of the lattice gauge theory. We prove that every dual configuration (or spin foam) can be equivalently described as a self--avoiding worldsheet of strings on a framing of the lattice. Using this correspondence, we translate the partition function into a sum over closed worldsheets that are weighted with explicit amplitudes. The expectation value of two Polyakov loops with spin j becomes a sum over worldsheets that are bounded by 2j strings along a framing of the loops.
hep-th↗
Two-dimensional phase transition models and λϕ^4 field theory
The overview is given of the results obtained recently in the course of renormalization-group (RG) study of two-dimensional (2D) models. RG functions of the two-dimensional n-vector λϕ^4 Euclidean field theory are written down up to the five-loop terms and perturbative series are resummed by the Pade-Borel-Leroy techniques. An account for the five-loop term is shown to shift the Wilson fixed point only briefly, leaving it outside the segment formed by the results of the lattice calculations. This is argued to reflect the influence of the non-analytical contribution to the β-function. The evaluation of the critical exponents for n = 1, n = 0 and n = -1 in the five-loop approximation and comparison of the results with known exact values confirm the conclusion that non-analytical contributions are visible in two dimensions. The estimates obtained on the base of pseudo-εexpansions originating from the 5-loop 2D RG series are also discussed.
cond-mat.stat-mech↗
Twist two operators at finite volume
We calculate the volume corrections to the two-pion matrix element of twist two operators.
hep-lat↗
The Schroedinger functional for Gross-Neveu models
Gross-Neveu type models with a finite number of fermion flavours are studied on a two-dimensional Euclidean space-time lattice. The models are asymptotically free and are invariant under a chiral symmetry. These similarities to QCD make them perfect benchmark systems for fermion actions used in large scale lattice QCD computations. The Schroedinger functional for the Gross-Neveu models is defined for both, Wilson and Ginsparg-Wilson fermions, and shown to be renormalisable in 1-loop lattice perturbation theory. In two dimensions four fermion interactions of the Gross-Neveu models have dimensionless coupling constants. The symmetry properties of the four fermion interaction terms and the relations among them are discussed. For Wilson fermions chiral symmetry is explicitly broken and additional terms must be included in the action. Chiral symmetry is restored up to cut-off effects by tuning the bare mass and one of the couplings. The critical mass and the symmetry restoring coupling are computed to second order in lattice perturbation theory. This result is used in the 1-loop computation of the renormalised couplings and the associated beta-functions. The renormalised couplings are defined in terms of suitable boundary-to-boundary correlation functions. In the computation the known first order coefficients of the beta-functions are reproduced. One of the couplings is found to have a vanishing beta-function. The calculation is repeated for the recently proposed Schroedinger functional with exact chiral symmetry, i.e. Ginsparg-Wilson fermions. The renormalisation pattern is found to be the same as in the Wilson case. Using the regularisation dependent finite part of the renormalised couplings, the ratio of the Lambda-parameters is computed.
hep-lat↗
Thermodynamical quantities for overlap fermions with chemical potential
Recently a formulation of overlap fermions at finite density based on an analytic continuation of the sign function was proposed. We study this proposal by analyzing the energy and number densities for free fermions as a function of the chemical potential and the temperature. Our results show that overlap fermions with chemical potential give rise to the correct continuum behavior.
hep-lat↗
Why rooting fails
I explore the origins of the unphysical predictions from rooted staggered fermion algorithms. Before rooting, the exact chiral symmetry of staggered fermions is a flavored symmetry among the four "tastes." The rooting procedure averages over tastes of different chiralities. This averaging forbids the appearance of the correct 't Hooft vertex for the target theory.
hep-lat↗
Quark Mass dependence at Two Loops for Meson Properties
This talks contains a short introduction to Chiral Perturbation Theory and the existing calculations to two-loop order in the mesonic sector. I include a discussion on which quantities the expansion can be organized in. The present best values of the Low-Energy-Constants as determined from continuum physics are given as well as the assumptions underlying the fits to experimental data. I present plots of masses, decay constants and $f_+(0)$ in $K_{\ell3}$ as a function of quark or meson masses. The talk ends with a list of things for which it would be extremely useful to have good results from lattice QCD calculations.
hep-lat↗
Roles of the quark field in the infrared lattice Coulomb gauge and Landau gauge QCD
The effective coupling of QCD is measured by using the gauge configurations produced by the MILC collaboration in which the Kogut Susskind (KS) fermion is incorporated and by using that produced by the QCDOC collaboration in which the domain wall fermion (DWF) is incorporated. We fix the gauge to the Landau gauge and to the Coulomb gauge. The infrared effective coupling in the Coulomb gauge agrees with the recent extraction at JLab, but that in the Landau gauge shows infrared suppression. The suppression is expected to be due to the color anti-symmetric ghost propagator which in the unquenched configurations has stronger infrared singularity than the color diagonal ghost propagator. The Coulomb form factor in the infrared depends on the kind of the fermion incorporated in the system and the temperature. The quark has the effect of quenching randomness and the fluctuation of the color anti-symmetric ghost propagator is reduced in the unquenched configuration, and the Kugo-Ojima parameter c is closer to 1 in the unquenched configuration than in the quenched configuration.
hep-lat↗